Author mcabbott
1 Star
Updated Last
11 Months Ago
Started In
January 2019


Build Status

] add ArrayAllez

⊙ = \odot

Matrix multiplication, on the last index of one tensor & the first index of the next:

three = rand(2,2,5);
mat = rand(5,2);

p1 = three ⊙ mat

p2 = reshape(reshape(three,:,5) * mat ,2,2,2) # same

using Einsum
@einsum p3[i,j,k] := three[i,j,s] * mat[s,k]  # same

There are also variants ⊙ˡ, ⊙ʳ with different gradient definitions, specifying that only what's on the left (or right) needs to be tracked. (Likewise *ˡ, *ʳ for ordinary *.)

bmm == ⨱ (\timesbar)

Batched matrix multiplication, which understands all trailing dimensions:

four = rand(2,3,8,9);
three = rand(3,8,9);

size(four ⨱ three) == (2, 8, 9)
(four ⨱ three)[:,1,1]  four[:,:,1,1] * three[:,1,1]

using Einsum
@einsum out[i,x,y] := four[i,j,x,y] * three[j,x,y];
out  four ⨱ three

Corresponding ⨱ˡ, ⨱ʳ are not yet defined.


Both and will propagate names from NamedDims.jl.

log! ∘ exp!

This began as a way to more conveniently choose between Yeppp! and AppleAccelerate and IntelVectorMath, without requiring that any by installed. The fallback version is just a loop, with @threads for large enough arrays.

x = rand(1,100);

y = exp0(x)  # precisely = exp.(x)
x  log!(y)  # in-place, just a loop

using AppleAccelerate  # or using IntelVectorMath, or using Yeppp

y = exp!(x)  # with ! mutates
x = log_(y)  # with _ copies

Besides log! and exp!, there is also scale! which understands rows/columns. And iscale! which divides, and inv! which is an element-wise inverse. All have non-mutating versions ending _ instead of !, and simple broadcast-ed versions with 0.

m = ones(3,7)
v = rand(3)
r = rand(7)'

scale0(m, 99)  # simply m .* 99
scale_(m, v)   # like m .* v but using rmul!
iscale!(m, r)  # like m ./ r but mutating.

These commands all make some attempt to define gradients for use with Tracker ans Zygote, but caveat emptor. There is also an exp!! which mutates both its forward input and its backward gradient, which may be a terrible idea.

using Tracker
x = param(randn(5));
y = exp_(x)

Tracker.back!(sum_(exp!(x))) == y # true

This package also defines gradients for prod (overwriting an incorrect one) and cumprod, as in this PR.


An experiment with LRUCache for working space:

x = rand(2000)' # turns off below this size

copy_(:copy, x)
similar_(:sim, x)
Array_{Float64}(:new, 5,1000) # @btime 200 ns, 32 bytes

inv_(:inv, x) # most of the _ functions can opt-in


This macro wraps reductions like sum(A; dims=...) in dropdims(). It understands things like this:

@dropdims sum(10 .* randn(2,10); dims=2) do x
    trunc(Int, x)

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